These teachings relate generally to multi-bit sigma-delta modulators (SDMs) and to analog-to-digital converters (ADCs) and digital-to-analog converters (DACs) that employ SDMs and, more specifically, relate to Dynamic Element Matching (DEM) algorithms and methods.
It is known to use Dynamic Element Matching (DEM) techniques in the context of sigma-delta converters and 1-bit data formats. Reference in this regard can be had to, for example, U.S. Pat. No.: 5,990,819, xe2x80x9cD/A converter and delta-sigma D/A converterxe2x80x9d, by Fujimori and to U.S. Pat. No.: 6,011,501, xe2x80x9cCircuits, systems and methods for processing data in a one-bit formatxe2x80x9d, by Gong et al. Dynamic element matching and sigma-delta modulator techniques are both well known in the art.
Single-bit SDMs are widely used in ADCs for the reason that they do not require accurate components, and can thus be readily implemented using modern CMOS integrated circuit processes. The single-bit DAC in the feedback loop is also readily implemented, as it is an inherently linear device. However, in order to obtain a wide dynamic range the single-bit SDM requires a high oversampling ratio (OSR) and/or a high modulator order, which typically requires a prohibitively large integrated circuit area and/or excessive power consumption to realize.
For stability reasons the dynamic range cannot be increased above a certain limit, at a low OSR, by simply increasing the modulator order. However, the dynamic range can be increased, without increasing the OSR or the modulator order, by increasing the number of quantization levels, i.e., by using a multi-bit SDM. The multi-bit SDM requires the use of a multi-bit DAC in the feedback loop.
However, multi-bit DACs are not inherently linear, and to achieve high accuracy (e.g., more than about 10 bits), either calibration or dynamic element matching (DEM) is often required.
A problem that is created by the use of some DEM algorithms, in particular a cyclic DEM algorithm, is a tonal behavior due to a limit cycle oscillation of the DEM in a multi-bit DAC application. Multi-bit DACs are used as basic building blocks in both oversampled ADCs and DACs.
The general structure of the multi-bit DAC 1 (without DEM), based on the use of thermometer coding, is shown in FIG. 1. Each bit of the digital thermometer input code (M bits, where M=2Nxe2x88x921) is converted into an analog signal by switching corresponding analog unit elements 2. The analog signals output by the unit elements 2 are summed at node 3 to form an analog output signal of the DAC 1. Unit elements are any circuit element that can be used for converting a digital signal to an analog form, i.e., a current, charge or voltage. For example, in a current steering DAC the unit elements are current sources or current mirrors, while in a switched capacitor DAC the unit elements are capacitors. Resistors can also be used as unit element implementations.
A significant disadvantage of the multi-bit DAC 1 shown in FIG. 1 is that variations between the unit elements 2, i.e., the mismatch error introduces nonlinearity into the digital to analog conversion. Through the use of a DEM algorithm this non-linearity can be converted to wide-band noise, or it can be concentrated into certain frequency bands by controlling the usage of the unit elements 2. All DEM algorithms are based on averaging the integral error in DA conversion due to the unit element mismatch error by averaging the use of the unit elements 2. Depending on the DEM algorithm efficiency, the power spectral density of the wide-band noise can be further shaped so that most of the noise is shifted outside of the signal band of interest. This principle of mismatch noise shaping is similar to noise shaping in SDMs.
FIG. 2 is a simplified block diagram of a conventional multi-bit DAC 5 that includes a switching matrix 6 controlled by a DEM algorithm block 7. The DEM block 7 could be, for example, one based on data weighted averaging (DWA) or rotation, such as clocked averaging (CLA). The feedback path from the output of the switching matrix 6, or from the outputs of the unit elements 2 (not shown), is required only for those DEM algorithms that maintain a record of the actual usage of the unit elements 2. The feedback path is generally required for noise shaping DEM algorithms.
General reference with regard to DWA may be had to a publication: Rex T. Baird, Terry S. Fiez, Linearity Enhancement of Multibit xcex94xcexa3 A/D and D/A Converters Using Data Weighted Averaging, IEEE Transactions on Circuits and Systemsxe2x80x94II: Analog and Digital Signal Processing, Vol. 42, No. 12, December 1995, and with regard to CLA reference can be made to Y. Sakina, Multibit xcexa3xe2x88x92xcex94 Analog to Digital Converters with Nonlinearity Correction Using Dynamic Barrel Shifting, M.A.Sc thesis, ERL, Univ. California at Berkeley, 1990.
The operational principle of averaging algorithms is shown in FIGS. 5A and 5B, which plot power spectral density (dB) versus frequency. More particularly, these Figures illustrate the performance comparison of different DEM algorithms in an ADC based on a 3rd order SDM with an 8-level internal DAC in the ADC feedback path. FIG. 5A shows the case of random data averaging (RDA) without DWA, while FIG. 5B shows the case of DWA. The undesirable generated tones are circled in FIG. 5B. General reference with regard to RDA can be made to a publication: L. Richard Carley, A Noise-Shaping Coder Topology for 15+Bit Converters, IEEE Journal of Solid-State Circuits, Vol. 24. No. 2, April 1989.
In cyclic DEM algorithms, such as rotation based clocked averaging (CLA) and DWA, the DAC mismatch error is converted into wide-band noise, but disadvantageously also exhibits periodic signal components, i.e., tones, at certain frequencies. This tonal behavior is found as well in other noise-shaping DEM algorithms, although the amplitude of the tones is generally less. The generation of tones is undesirable as they tend to degrade the spurious free dynamic range, demodulate out-of-band noise to the desired signal band, and also disturb signals in the desired signal band. The tones may also become audible in an audio converter application, even when they are below the noise floor. In general, the DWA algorithm contains first order noise shaping, while the CLA algorithm has a white noise floor.
It has been known in the art to modify the DWA algorithm in an attempt to control tonal behavior. Known types of modifications are: (a) adding a dither signal to the DWA algorithm, (b) using the rotated data weighted averaging (RDWA) algorithm; and (c) the use of additional unit elements. The modifications (a) and (b) serve to decompose the unwanted tones, while the modification (c) shifts the tones in frequency, but does not decompose them.
However, there are drawbacks to the use of these conventional techniques. For example, adding the dither signal has the disadvantage of increasing the noise floor. Additionally, in the DWA algorithm the dither signal also introduces the white noise floor near DC, which has the effect of removing the first order noise shaping at low frequencies, and thus degrades overall performance.
With regard to the RDWA algorithm, various sequences are present that are changed occasionally. In higher level DACs the number of possible sequences produces unmanageable complexity, and thus the total number of possible sequences must be limited. Furthermore, too frequent switching of the sequences increases the noise floor at frequencies near DC significantly. The approach of adding additional unit elements increases both the required circuit area and the power consumption, both of which are undesirable.
Tone cancellation is important in high resolution RF and audio converters, where the use of the DWA and other noise-shaping DEM algorithms is usually desired to achieve a high dynamic range. As such, it can be appreciated that it is very desirable to suppress or cancel the generation of tones in order to obtain a high signal to noise and distortion ratio (SNDR) and spurious free dynamic range (SFDR), and to do so without incurring the problems that arise in conventional approaches to tonal cancellation.
The foregoing and other problems are overcome by methods and apparatus in accordance with embodiments of these teachings. These teachings provide a technique to suppress or cancel the generation of tones for cyclic DEM algorithms, such as the DWA and CLA algorithms. The circuitry can be implemented entirely in the digital domain, thereby making the incorporation of these teachings into integrated circuit applications particularly straightforward. These teachings also do not require an increase in the number of analog circuit components, thereby conserving integrated circuit area and power consumption.
The preferred method and apparatus is based on a two step or two stage DEM algorithm. The primary DEM algorithm is preferably a cyclic algorithm that converts the mismatch distortion to wide-band noise and tones, while the secondary DEM algorithm converts the tones to wide-band noise. The secondary DEM algorithm does not decompose the averaging performed by the primary DEM algorithm, and thus the noise shaping of the primary DEM algorithm is preserved.
In the preferred embodiment a connection between the primary DEM algorithm processor block and the unit elements is randomized within a switching matrix of the secondary DEM algorithm. The operation of the secondary DEM algorithm is synchronized to the operation the primary DEM algorithm, and thus the random switching applied by the secondary DEM algorithm does not decompose the averaging of the primary DEM algorithm. In this manner the noise shaping and the long term averaging applied by the primary DEM algorithm is preserved, and the white noise floor near DC does not occur. These are important considerations in maintaining the performance of the DWA algorithm.
The operation of the improved DEM technique in accordance with these teachings converts the unwanted tones to noise-shaped wide-band noise, and does not simply shift the unwanted tones to frequencies outside of the signal band of interest. As a result, the out-of-band noise is not demodulated into the signal band of interest due to the high frequency tones produced by the DEM algorithm. The noise shaping of the primary DEM algorithm is also preserved, without introducing the white noise floor. This is because the switching of the secondary DEM algorithm is synchronized to the primary DEM algorithm, resulting in a preservation of the long term averaging afforded by the primary DEM algorithm.
A further advantage realized by the practice of these teachings is that a simple implementation of the first order noise shaping of the DWA algorithm is achieved, without requiring a significant increase in circuit area due to sorting circuitry that is typically required in pure noise shaping algorithms.